WASHINGTON, Sept 4 (Reuters) - Giving another chance to a key part of the Obamacare health law, a U.S. appeals court on Thursday threw out a decision it made in July that threatened to limit the availability of federal health insurance subsidies for millions of people.

The U.S. Court of Appeals for the District of Columbia Circuit agreed to rehear the question of whether the subsidies should be available in all 50 states or only in some. The court will hear new oral arguments on Dec. 17.

The U.S. Justice Department had asked for the rehearing after a three-judge panel on the court ruled against the Obama administration on the legality of the subsidies, which have been challenged by conservatives who object to the 2010 healthcare law.

A panel of up to 13 judges will reconsider the case, improving the administration's odds of a more favorable outcome because Democratic appointees make up a majority of the court, legal experts said.

A senior White House official welcomed the court's action, saying it was "an important and welcome next step."

The court's announcement also delayed possible U.S. Supreme Court consideration of the issue.

Obamacare, the most sweeping overhaul of the healthcare system in decades and the signature domestic accomplishment of President Barack Obama's first term, set up health insurance exchanges and tax-credit subsidies to help people afford insurance premiums.

The law is still a target of criticism by Republicans.

Sam Kazman, general counsel of the Competitive Enterprise Institute, which is funding the litigation against Obamacare, said that ultimately the Supreme Court "is the only court that can resolve this issue in the quick and final manner that the country deserves."

The plaintiffs say that, based on the language in the law, the subsidies may only be paid in states that have their own online health insurance exchanges. A total of 36 states do not have exchanges of their own.

Five million people could be affected, analysts have estimated, if the administration loses the legal fight and subsidies disappear from the federal marketplaces that have been set up in states that did not create their own exchanges.

The decision to rehear the case was made by the court's 11 active judges. Two senior judges who were part of the original three-judge panel are also likely to participate in the rehearing. One is a Republican appointee and one a Democratic appointee.

The three-judge panel that ruled in July was split 2-1, with two Republican appointees in the majority.

In a similar case involving Obamacare subsidies, the 4th U.S. Circuit Court of Appeals in Richmond, Virginia, ruled in favor of the Obama administration in July. The plaintiffs in that case have already sought immediate U.S. Supreme Court review of that ruling.

The case before the Washington court is Halbig v. Burwell, U.S. Court of Appeals for the District of Columbia Circuit, No. 14-5018. (Editing by Doina Chiacu, Kevin Drawbaugh, Bernadette Baum and Paul Simao)